Turbo and convolutional codes are widely used forward error correction codes. Turbo codes were proposed by Berrou and Glavieux in 1993 and have been adopted in many communication standards such as Wideband-CDMA (WCDMA), Code Division Multiple Access 2000 (CDMA2000), Worldwide Interoperability for Microwave Access (WiMAX), Long Term Evolution (LTE) and Digital Video Broadcasting-Return Channel via Satellite (DVB-RCS). The codes allow near optimal decoding with excellent performance approaching the Shannon limit for Additive White Gaussian Noise (AWGN) channels.
Conventional radix-4 decoding supports duo-binary turbo codes (adopted in WiMAX and DVB-RCS) and single-binary convolutional and turbo codes. Moreover, support for the duo-binary turbo codes implies two times faster decoding techniques than for single-binary codes at the expense of some additional circuit area. A problem with radix-4 decoding is a bottleneck in calculating the state metrics. A State Metrics Calculator (SMC) circuit performing add-compare-select operations experiences a bottleneck when implementing high-speed convolutional and turbo decoders. State metrics calculations cannot be easily pipelined because the state metrics computed at time instance t are used for computing the state metrics at time instance t+1. Therefore, radix-4 decoding increases the importance of the path through the SMC circuit. Another problem with radix-4 decoding is related with decoder universality (i.e., the ability to support many different convolutional and turbo codes in the same hardware). Since the trellises for the various codes are different, additional configuration logic (i.e., multiplexers) is commonly used in the SMC circuit to handle all of the trellises in a single design.